Designing nonlinear control systems is still difficult so many researchers are trying to findsome useful ways and methods to solve this problem. As a result of such research, some methodshave been seen trying to design a good enough control system for nonlinear plants. But a disadvantageof these methods is the complexity, so it created a need to compare some methods to determinewhich one is the easiest method to design a control system for nonlinear plants. It wasfound a way to compare two methods, which is comparing the regions of initial conditions of thesystems which are designed using these methods. Two analytical nonlinear control systems designmethods are compared on the example of the design control systems mobile robots. The algebraicpolynomial-matrix method uses a quasilinear model, and the feedback linearization method usesparticular feedback. Both considered methods give a bounded domain of equilibrium attraction,therefore the obtained control systems can be operated only with bounded initial conditions.The numerical example of designing the control systems for one object by these methods and theestimates of the attraction areas of the system’s equilibriums of these systems are given in thepaper. As a result of this paper, it was found that using the algebraic polynomial-matrix methodwill get a bigger cross section of initial conditions of the plant’s variable than the same cross sectionwhich is given by the feedback linearization method.